Method and apparatus for improving MEMs accelerometer frequency response

ABSTRACT

Sensor apparatus and methods for operating the same for measuring acceleration are disclosed. In some embodiments, circuitry inside a sensor digitizes a measured acceleration signal from an accelerometer into a digitized acceleration signal, which is processed by a digital equalization filter within the sensor to provide an equalized acceleration signal. The equalized acceleration signal may have a frequency response that is substantially flat over a frequency range that extends beyond the resonant frequency of a MEMs sensor within the accelerometer of the sensor.

The present application relates to digital processing of sensor signals.

BACKGROUND

Sensors operate by detecting a change in a sensed condition, and outputelectrical signals representing the sensed condition. The sensedcondition may include acceleration, velocity, pressure, or othermechanical or environmental conditions. The output electrical signal isa time-domain signal that reflects how the sensed condition changesversus time. The output electrical signal can also be represented in thefrequency domain in terms of magnitude and frequency. The magnitude ofthe output electrical signal can be influenced by characteristics of theprocessing circuitry that receives the sensor output. It is desirable,in many applications, to use the processing circuitry to enhance thefrequency response of the sensor element. The enhancement is in the formof magnitude adjustment, so that the bandwidth of the sensor is widened.

SUMMARY OF THE DISCLOSURE

Sensor apparatus and methods for operating the same for measuringacceleration are disclosed. In some embodiments, circuitry inside asensor apparatus digitizes a measured acceleration signal from anaccelerometer into a digitized acceleration signal, which is processedby a digital equalization filter within the sensor to provide anequalized acceleration signal. The equalized acceleration signal mayhave a frequency response that is substantially flat over a frequencyrange that extends beyond the resonant frequency of a MEMs sensor withinthe accelerometer of the sensor apparatus.

In some embodiments, a method for operating a sensor apparatus isprovided. The sensor apparatus comprises an accelerometer. Theaccelerometer has a microelectromechanical system (MEMs) sensor. Themethod comprises measuring an acceleration signal at an output of theaccelerometer; generating a digitized acceleration signal based on theacceleration signal; and processing, with a digital equalization filter,the digitized acceleration signal to generate an equalized accelerationsignal.

In some embodiments, a sensor apparatus is provided. The sensorapparatus comprises an accelerometer having a microelectromechanicalsystem (MEMs) sensor; a non-volatile memory configured to store one ormore coefficients representing one or more mechanical characteristics ofthe MEMs sensor; circuitry that is configured to measure an accelerationsignal at an output of the accelerometer and to generate a digitizedacceleration signal based on the acceleration signal. The sensorapparatus further comprises a digital equalization filter configured togenerate an equalized acceleration signal based on the digitizedacceleration signal.

In some embodiments, a sensor system is provided. The sensor systemcomprises an accelerometer having an output; and means for equalizing anacceleration signal at the output.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects and embodiments of the application will be describedwith reference to the following figures. It should be appreciated thatthe figures are not necessarily drawn to scale. Items appearing inmultiple figures are indicated by the same reference number in all thefigures in which they appear. In the drawings:

FIG. 1 is a high-level block diagram of a sensor apparatus, according tosome embodiments;

FIG. 2 is a simulated data chart illustrating frequency response curvesof several exemplary sensors, in accordance with some embodiments;

FIG. 3 is a flow diagram of an exemplary process for performing digitalequalization, in accordance with some embodiments;

FIG. 4 is a flow diagram of an exemplary process to perform digitalequalization with digital equalization filter, in accordance with someembodiments;

FIG. 5 is a flow diagram of an exemplary process to perform digitalequalization of an acceleration signal while providing temperaturecompensation, in accordance with some embodiments;

FIG. 6 is a block diagram illustrating components of the circuitry andthe digital equalization filter, in accordance with an exemplaryembodiment;

FIG. 7 is a schematic diagram of an electronic device that houses one ormore sensor of the type as disclosed in the present application.

DETAILED DESCRIPTION

Aspects of the present application are directed to a sensor apparatusfor measuring an acceleration of the sensor. The inventor hasappreciated and recognized that in certain applications, such asdetecting acoustic vibrations related to speech, it is desirable for thefrequency response of the measured acceleration to be substantially flatover a wide range of frequencies. The inventor has also recognized thatin a sensor based on a MEMs accelerator having a MEMs sensor, theflatness of the frequency response of the measured acceleration is oftendictated by the measurement bandwidth of the MEMs accelerator, which initself is affected by the resonant behavior of the MEMs sensor such asits resonant frequency f₀ and quality factor Q.

As an example of a measurement bandwidth of a MEMs accelerator, it mayonly have a relatively flat frequency response from very low frequencyof close to direct current (DC), to approximately f₀/3. While choosing aMEMs sensor having a greater f₀ may increase the measurement bandwidth,doing so has other undesirable consequences. For example, a higher f₀will increase noise at the accelerator output, because noise isproportional to the square of f₀. Therefore, it is desirable to keepf_(o) at a relatively low frequency for a low noise accelerator.However, with a low frequency f₀, the frequency response tends to peakup rapidly beyond the measurement band towards the resonance peak due tothe Q factor. Therefore the inventor has recognized a need to extend themeasurement bandwidth and improve the flatness of the frequency responseof a low noise accelerometer, preferably in a frequency range beyond theresonance peak at f₀. Aspects of the present application are directed toa solution to such a need.

In some embodiments, circuitry inside a sensor apparatus digitizes ameasured acceleration signal from an accelerometer into a digitizedacceleration signal, which is processed by a digital equalization filterwithin the sensor to provide an equalized acceleration signal. Theequalized acceleration signal may have a frequency response that issubstantially flat over a frequency range that extends beyond the f₀ ofa MEMs sensor within the accelerometer of the sensor apparatus.

The inventor has recognized and appreciated that while it is possible toperform equalization of an analog output signal of the accelerometer,such analog equalization has several drawbacks compared to the digitalequalization as disclosed herein. For example, accelerometer componentsare prone to have variations in parametric values, due to themanufacturing process and environmental stress during operation. Analogequalization using analog circuitry suffers from component parameterdrift due to process, supply and temperature variation, thus cannotmaintain an accurate equalization at all time. Furthermore, analogcircuitry often include discreet passive components such as capacitorsand inductors that may be more complex and costly to manufacturecompared to digital circuitry that can be implemented as integratedcircuit on a semiconductor die.

According to an aspect of the present application, digital equalizationis performed on an digitized acceleration signal, rather than avelocity, displacement, or sound power in the case of acousticvibrations. The inventor has appreciated and recognized that velocityand displacement may be derived from acceleration signals by performingone or more levels of integrations. Because the un-equalized MEMs sensorhas a significant boost in frequency response at f₀, noise picked up bythe accelerometer will be amplified in the accelerometer output aroundf₀. By equalizing the acceleration signal to have a flat frequencyresponse prior to integration, the effect of noise boost around theresonant peak may be reduced in subsequent processing stages, whichresult in a low-noise sensor output across a broad measurementbandwidth.

In some embodiments, the digital equalization filter may utilize atransfer function of the MEMs sensor to equalize the digitalacceleration signal. The transfer function may be represented by aformula based on f₀ and Q of the MEMs sensor, and coefficients of theformula may be stored in a non-volatile memory of the sensor apparatusfor use by the digital equalization filter during operation of thesensor. Each MEMs sensor may be characterized, for example with atester, to obtain its f₀ and Q during manufacturing process.

In some embodiments, the digital equalization filter may be used inconjunction with a temperature sensor located adjacent theaccelerometer. In such embodiments, a predictive model of theaccelerometer response variation versus temperature may be used by thedigital equalization filter to perform corrective processing of thedigital acceleration signal to reduce or eliminate the temperaturedependence of the MEMs sensor output.

In some embodiments, digital equalization may be performed by firstobtaining an inverse transfer function of the MEMs sensor by a group ofcascaded digital filters. The digitized acceleration signal outputted bythe MEMs accelerometer can then be convolved with the impulse responsesof the cascaded digital filters to obtain an equalized accelerationsignal with a flat frequency response so that the effective measurementbandwidth can be extended beyond the resonant frequency f₀.

FIG. 1 is a high level block diagram of a sensor apparatus 10, accordingto some embodiments. Sensor apparatus 10 comprises an accelerometer 100having a MEMs sensor 110, circuitry 120, a digital equalization filter130, a non-volatile memory 140, and optionally a temperature sensor 150.Sensor apparatus 10 also may optionally comprise one or more integrators160. Accelerometer 100 may also be referred to as a MEMs accelerometer.

In FIG. 1 , MEMs sensor 110 may be a mechanical sensor fabricated usingMEMs technology known in the art. MEMs sensor 110 may comprise one ormore proof masses that are movably attached to a support substrate,allowing the proof masses to move in response to external electricand/or mechanical stimuli. MEMs sensor 110 may be of any suitablegeometry, material, and transduction mechanism, as aspects of thepresent application are not so limited. In one non-limiting example,MEMs sensor 110 is part of a low noise, low-g accelerometer that has af₀ of a few kHz.

Accelerator 100 may comprise a number of active and passive electroniccomponents to provide power and control signals to MEMs sensor 110, andto collect electrical signals in response to motion. In someembodiments, MEMs sensor 110 is a quasi-static mechanical resonator thathas high dissipation and low Q, and operates as a very lossy resonator,although aspects of the present application is not so limited. In someother embodiments, MEMs sensor 110 may be a high-Q resonator driven by adriving signal to resonate at a resonant frequency f₀. In response to anacceleration, accelerator 100 may generate an acceleration signal 112 atan accelerator output 114. Acceleration signal 112 may have an amplitudethat varies both in time domain and in frequency domain based on the amechanical acceleration α of the MEMs accelerator 100. The mechanicalacceleration may be a linear acceleration of the sensor 10 along anylinear axis, or an angular acceleration along any axis.

Mechanical acceleration α may have different frequency components α(ω),where ω is the frequency. Without wishing to be bound by a particulartheory, accelerator 100 may have a resonance response curvecharacterized by a transfer function H(ω):H(ω)=ω₀ω/ω²+ω₀ /Qω+ω ₀ ²  (Eq. 1),where ω₀=2πf₀ is the resonant angular frequency of the MEMs sensor 110,and Q is its quality factor. f₀ and Q are characteristic mechanicalproperties of the MEMs sensor 110, and may be characterized usingmethods known to a person of ordinary skill in the art on theaccelerator 100. Acceleration signal 112 is proportional to H(ω)·α(ω),and has a relatively flat frequency response at a low frequency range,where the transfer function H(ω) does not vary significantly over ω. Insuch a low frequency range, the accelerometer may be considered a goodlinear transducer of mechanical acceleration, and the frequency rangemay be considered a usable range. When ω increases to approach resonancehowever, H(ω) peaks up rapidly and acceleration signal 112 may no longerbe a good representation of the mechanical acceleration. An example ofthe frequency response in acceleration signal 112 is illustrated in FIG.2 .

FIG. 2 is a simulated data chart 20 illustrating frequency responsecurves of several exemplary sensors, in accordance with someembodiments. Curve 212 is a simulated magnitude (measured in unit ofdecibel or dB) versus frequency curve that may be a frequency responseof an acceleration signal such as signal 112 in FIG. 1 . To simulatecurve 212, a MEMs sensor having f₀=5.8 kHz and Q=3.5 is used, which istypical for a low-noise, low-g resonator.

As shown in FIG. 2 , curve 212 is relatively flat with a magnitudevariation of no more than 1 dB in the frequency range of between zero toabout 1.5 kHz, and relatively flat with a magnitude variation of no morethan 3 dB in the frequency range of between zero to about 3 kHz. Above 3kHz, the frequency response increases quickly to peak at more than 10 dBapproaching f₀ due to the shape of the resonance transfer function.Therefore for the resonator in this example, the usable frequency rangeis only 1.5 kHz if a flatness of no more than 1 dB is desired, or only 3kHz if a flatness of no more than 3 dB is desired.

Aspects of the present application is directed to a digital equalizationtechnique that may provide a usable frequency response range from DC tobeyond f₀, or beyond 5.8 kHz in the example of curve 212 as shown inFIG. 2 .

Referring back to the embodiment shown in FIG. 1 , circuitry 120measures the analog acceleration signal 112 at the accelerator output114, and generates a digitized acceleration signal 122 that representsthe acceleration signal 112. Circuitry 120 may include ananalog-to-digital converter (ADC) of a type that is known in the art.

Still referring to FIG. 1 , digital equalization filter 130 receives thedigitized acceleration signal 122 from circuitry 120, and generates anequalized acceleration signal that is based on the digitizedacceleration signal 122, but has an expanded usable frequency rangehaving a desired flat frequency response throughout. The inventor hasrecognized and appreciated that

FIG. 3 is a flow diagram of an exemplary process 300 for performingdigital equalization, in accordance with some embodiments. At act 302 ofprocess 300, circuitry 120 measures acceleration signal 112 at output114 of accelerometer 100. At act 304, circuitry 120 generates digitizedacceleration signal 122 based on acceleration signal 112. At act 306,digital equalization filter 130 processes the digitized accelerationsignal 122 to generate an equalized acceleration signal 132, which maybe provided as an output of sensor 10.

Optionally and as shown in FIG. 1 , sensor 10 comprises one or moreintegrator 160. As shown in FIG. 3 , at act 308, integrator 160integrates the equalized acceleration signal 132 and generates an outputsignal 162 based on a time integral of equalized acceleration signal132. In some embodiments, equalized acceleration signal 132 isintegrated once to represent a velocity signal. In some embodiments,equalized acceleration signal 132 is integrated twice to represent adisplacement signal. In one non-limiting example, sensor 10 isconfigured to sense an acoustic signal such as a human utterance ormusic. In such an example, an equalized acceleration signal isintegrated twice to obtain a displacement signal across a usablefrequency range that spans to 10 kHz or above. The integratedacceleration signal may be representative of a sound pressure, or soundpower of the acoustic signal.

The inventor has recognized and appreciated that if the transferfunction of the MEMs sensor is predetermined, the transfer function canbe used in the digital equalization filter to process the sensed signalto suppress the resonator's peaking behavior around f₀ in the digitaldomain.

FIG. 4 is a flow diagram of an exemplary process 400 to perform digitalequalization with digital equalization filter 130, in accordance withsome embodiments.

At act 410 of process 400, mechanical characteristics such as resonantfrequency f₀ and quality factor Q of the MEMs sensor 110 is measured.Measurement of f₀ and Q may be carried out as part of manufacturingprocess, prior to packaging sensor 10 for sale and use by the customer.Alternatively or additionally, f₀ and Q may be characterized aftermanufacturing, for example with a tester when assembling sensor 10 aspart of an electronic device. The measured f₀ and Q may be stored insensor 10, for example in at least one non-volatile memory 140 as shownin FIG. 1 . It should be appreciated that it is not a requirement thatthe non-volatile memory 140 stores the raw values of f₀ and Q. In theembodiment shown in FIG. 4 , act 410 also comprises computing a transferfunction of the MEMs sensor based on a pre-determined formula such asEq. 1 using the measured f₀ and Q. The computation may be performed inan external processor such as a computer in the tester that measures f₀and Q, although aspects of the present application is not so limited.

At act 411, coefficients that represent the fitting parameters of thetransfer function may be stored in the non-volatile memory. It should beappreciated that the coefficients may also be fitting parameters of arepresentation of the transfer function, and not the transfer functionitself. In some embodiments, an equalization (EQ) curve that is theinverse of the transfer function may be computed, and fitting parametersof the EQ curve may be stored at act 411 as the coefficients. Thecoefficients may be, for example, quadratic or higher order polynomialcurve fitting coefficients.

At act 412, the digital equalization filter 130 reads the one or morestored coefficients from the at least one non-volatile memory 140.Reading of the coefficients may be performed only once during devicepower up to save power.

At act 414, a representation of the transfer function of the MEMs sensoris constructed based on the one or more stored coefficients in the atleast one non-volatile memory 140. For example, the EQ curve may beconstructed at this act to represent the transfer function. Theconstruction may be performed using processors within the digitalequalization filter 130 using a pre-determined formula.

At act 416, digital equalization filter 130 convolves the digitizedacceleration signal 122 with an impulse response of the representationof the transfer function to generate the equalized acceleration signal132. According to some embodiments, it is not necessary to compute theimpulse response of the EQ curve, if it is comprised of several stagesin cascade. In such embodiments, the input digitized acceleration signaldata sequence is computed as it enters and exits each session of theequalizer.

Aspects of the present application are also directed to using thedigital equalization filter to correct temperature compensation of theMEMs sensor. The inventor has recognized and appreciated that mechanicalcharacteristics of the MEMs sensor are susceptible to temperaturevariations during operation. For example, f₀ and Q of the MEMs sensormay drift as a function of temperature. In some embodiments, atemperature sensor 150 may be provided in a sensor, as shown in FIG. 1 .The temperature sensor 150 may be disposed adjacent to the accelerator100 and preferably, adjacent the MEMs sensor 110 to measure thetemperature of the movable mass within the accelerometer.

FIG. 5 is a flow diagram of an exemplary process 500 to perform digitalequalization of an acceleration signal while providing temperaturecompensation, in accordance with some embodiments. Process 500 issimilar in many aspects to process 400 as shown in FIG. 4 , with likenumerals representing similar acts.

Process 500 differs from process 400 in that after act 412, the processproceeds to act 513, where a temperature of the accelerometer ismeasured. At act 514, a representation of the transfer function of theMEMs sensor is constructed based not only on the one or more storedcoefficients, but also on the measured temperature. Atemperature-compensated predictive model of the MEMs sensor may becreated in the form of a polynomial fitting formula with coefficientsthat can provide a compensated f₀ and Q based on the measuredtemperature. Other means for providing temperature compensation may alsobe used, such as storing a look up table in the non-volatile memory,with entries of the look up table representing pre-calibrated f₀ and Qvalues at each temperature.

At the end of process 500, after the digitized acceleration signal isconvolved with an impulse response of the representation of the transferfunction at act 416 to generate the equalized acceleration signal, theprocess may optionally go back to act 513 to take another measurement oftemperature. The measured temperature may be stored in a volatilememory, and used in subsequent acts 514 and 416 to provide digitalequalization with continuously updated temperature readings. In someembodiments, act 513 may be repeated at a regular interval of timeduring operation of sensor 10.

Digital equalization filter 130 may be implemented with any suitabledigital circuit design known in the art, and may be integrated withcircuitry 120 on a same semiconductor substrate. In some embodiments,digital equalization filter may be implemented with a cascade ofmultiple digital filters. In one embodiment, the digital equalizationfilter can be implemented by the droop correction filter in a decimationfilter since at higher data rate (which is available in a multi-ratedecimation filter design), coefficients for the transfer function of theMEMs sensor can be computed more efficiently with smaller word-width.

Referring back to the data chart 20 in FIG. 2 . Curve 232 is a simulatedfrequency response of an equalized acceleration signal such as signal132 in FIG. 1 . Compared to curve 212 representing the frequencyresponse of the non-equalized acceleration signal 112, curve 232 showsthat the peaking magnitude around f₀=5.8 kHz has been flattened to beclose to zero dB. Significantly, curve 232 has an extended frequencyrange between 0 (or DC) and 8 kHz in which the frequency response isrelatively flat with a magnitude variation of no more than 3 dB, and anextended frequency range between 0 and 7 kHz in which the frequencyresponse is relatively flat with a magnitude variation of no more than 1dB. Therefore the usable frequency range of an accelerator having MEMssensor of the type as simulated in FIG. 2 can be expanded from 1.5 kHzto 7 kHz or more.

FIG. 2 also shows curves 231, 233, which represent simulated frequencyresponses of intermediate results of the digital equalization filter.Curve 231 shows the compensation effect of a droop filter, which hasflattened response both to the left side and the right side of f₀. Curve233 shows the compensation effect of a notch filter, which has a dipcentered around f₀. The combination of curves 212, 231 and 233contribute to the equalized acceleration signal represented by curve232.

FIG. 6 is a block diagram illustrating components of the circuitry andthe digital equalization filter, in accordance with an exemplaryembodiment. FIG. 6 shows a ADC 620, an Infinite Impulse Response (IIR)low-pass filter (LPF) 624, a sensor correction filter 630 and a timedivision multiplexing (TDM) port 634.

In FIG. 6 , ADC 620 may be part of circuitry 120 as shown in FIG. 1 ,and generates a digitized acceleration signal 622 at an output thatrepresents a measured analog acceleration signal in an accelerometersuch as accelerometer 100. The sampling rate f_(s) for signal 622 may be384 or 192 kHz in one non-limiting example.

LPF 624 is a digital filter that may process digitized accelerationsignal 622 to reduce the data rate using for example 24-96× decimation.The result is an intermediary digital signal 626. In the example abovewith f_(s) for signal 622 being 384 or 192 kHz, intermediary digitalsignal 626 may have a data rate of 8 kHz or 4 kHz. Filter 624 may alsoemploy a droop filter, which corrects the droop in the frequencyresponse, and contributes to flattening the frequency response around f₀in the digitized acceleration signal 622. Therefore a digitalequalization filter in accordance with aspects of the presentapplication may include a digital filter such as LPF 624.

Sensor correction filter 630 may read stored second order coefficientsfor the resonator transfer function from a non-volatile memory and applythe coefficients to perform filtering on the intermediate digital signal626 to generate an equalized acceleration signal 632, using methodsdiscussed above, such as process 400 as shown in FIG. 4 . The outputtedequalized acceleration signal 632 is then passed to TDM port 634 forfurther processing.

FIG. 7 is a schematic diagram of an electronic device 700 that housesone or more sensor 70 of the type as disclosed in the presentapplication. According to an aspect of the present application, a sensor70 having low-g MEMs accelerator may be provided in a wearableelectronic device 700 as shown in FIG. 7 to measure acoustic signals 74,such as human voice, music, or other audio emissions. Sensor 70 may havecomponents similar to sensor 10 that are configured to be operated in asimilar fashion with sensor 10 as described above. Wearable electronicdevice 700 may be an earphone, a headset, or a part of a smartphone. Inone example, wearable electronic device 700 may also have an acoustictransducer 72 such as a microphone for directly measuring acousticsignals. Microphone 72 may be turned off to save battery power, with theintention to be reactivated upon detection of a voice. However, in anoisy environment, it may be difficult for traditional microphones orsensors to differentiate the onset of human utterance from thebackground acoustic emissions. Sensor 70 may be able to detect alow-level acoustic signal using a low-noise MEMs accelerator, and towake up microphone 72 for continued measurement of the acoustic signal.In such an application, overall battery life of the electronic device700 may be reduced as there is no need for microphone 72 to be operatingcontinuously.

The technology described herein may be used in various settings,including those in which accelerometers are used. For example, consumerportable electronics, automotive, industrial automation and control,instrumentation and measurements, and healthcare applications may allmake use of the technology described herein.

The terms “approximately” and “about” may be used to mean within ±20% ofa target value in some embodiments, within ±10% of a target value insome embodiments, within ±5% of a target value in some embodiments, andyet within ±2% of a target value in some embodiments. The terms“approximately” and “about” may include the target value.

What is claimed is:
 1. A method for operating a sensor apparatuscomprising an accelerometer having a microelectromechanical systems(MEMs) sensor with a resonant frequency (f₀), the method comprising:measuring an acceleration signal at an output of the accelerometer;generating a digitized acceleration signal based on the accelerationsignal; and processing, with a digital equalization filter, thedigitized acceleration signal to generate an equalized accelerationsignal having a frequency response that is equalized over a frequencyrange that extends from 0 to f₀, wherein: the equalized accelerationsignal has a magnitude frequency response that varies by no more than 3decibels in the frequency range.
 2. The method of claim 1, wherein themagnitude frequency response varies by no more than 1 decibel in thefrequency range.
 3. The method of claim 1, wherein processing thedigitized acceleration signal comprises: convolving the digitizedacceleration signal with an impulse response of a representation of atransfer function of the MEMs sensor.
 4. The method of claim 3, whereinprocessing the digitized acceleration signal further comprises:constructing the representation of the transfer function of the MEMssensor based on one or more coefficients stored in at least onenon-volatile memory of the sensor.
 5. The method of claim 4, furthercomprising: measuring the f₀ and a quality factor (Q) of the MEMssensor; computing a transfer function of the MEMs sensor based on themeasured f₀ and Q; storing one or more coefficients representing thetransfer function in the at least one non-volatile memory.
 6. The methodof claim 4, further comprising measuring a temperature of theaccelerometer, and wherein constructing the representation of thetransfer function of the MEMs sensor is based on the one or morecoefficients and the measured temperature.
 7. The method of claim 1,further comprising integrating the equalized acceleration signal togenerate an output signal representing an acoustic signal received bythe accelerometer.
 8. The method of claim 1, wherein generating thedigitized acceleration signal comprises: sampling the accelerationsignal with an analog-to-digital converter to generate a sampled signal;processing the sampled signal with a decimation filter; and generatingthe digitized acceleration signal based on an output of the decimationfilter.
 9. A sensor apparatus comprising: an accelerometer having amicroelectromechanical systems (MEMs) sensor with a resonant frequency(f₀); a non-volatile memory configured to store one or more coefficientsrepresenting one or more mechanical characteristics of the MEMs sensor;circuitry configured to: measure an acceleration signal at an output ofthe accelerometer; generate a digitized acceleration signal based on theacceleration signal; and a digital equalization filter configured togenerate an equalized acceleration signal based on the digitizedacceleration signal, wherein the equalized acceleration signal has afrequency response that is equalized over a frequency range that extendsfrom 0 to f₀, wherein: the equalized acceleration signal has a magnitudefrequency response that varies by no more than 3 decibels in thefrequency range.
 10. The sensor apparatus of claim 9, wherein thedigital equalization filter is configured to generate an impulseresponse of a transfer function of the MEMs sensor based on the one ormore coefficients, and to generate the equalized acceleration signal byconvolving the digitized acceleration signal with the impulse response.11. The sensor apparatus of claim 10, wherein the one or morecoefficients comprise f₀ and a quality factor.
 12. The sensor apparatusof claim 10, further comprising a temperature sensor, and wherein: thedigital equalization filter is further configured to construct thetransfer function of the resonator based on the one or more coefficientsand a temperature of the accelerometer as measured by the temperaturesensor.
 13. The sensor apparatus of claim 9, further comprising anintegrator configured to generate an output signal representing anacoustic signal received by the accelerometer by integrating theequalized acceleration signal.
 14. The sensor apparatus of claim 9,wherein the circuitry comprises: an analog-to-digital converter coupledto the output of the resonator and configured to generate a sampledsignal; a decimation filter coupled to the analog-to-digital converterand configured to generate the digitized acceleration signal at anoutput of the decimation filter.
 15. The sensor apparatus of claim 9,further comprising an integrated circuit, wherein the circuitry and thedigital equalization filter are part of the integrated circuit.
 16. Asensor system, comprising: an accelerometer having an output and amicroelectromechanical systems (MEMs) sensor with a resonant frequency(f₀); an integrated circuit configured to: measure an accelerationsignal at the output of the accelerometer; generate a digitizedacceleration signal based on the acceleration signal; and a digitalequalization filter configured to generate an equalized accelerationsignal based on the digitized acceleration signal, wherein the equalizedacceleration signal has a frequency response that is equalized over afrequency range that extends from 0 to f₀, wherein: the equalizedacceleration signal has a magnitude frequency response that varies by nomore than 3 decibels in the frequency range.